Help deriving this elliptical orbit equation?

[skiz]

help deriving this elliptical orbit equation??

Hi guys, this is my first post on these boards. just found out about this forum and I am really happy because i often find i need a place like this to ask questions and my prayers are answered!

im a physics/computer science major in my second year at the University of the Witwatersrand in Johannesburg, South Africa.

any way.. enough history..

i need help deriving this equation for an elliptical orbit :

$$\frac{(x + ae)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$

where e is the eccentricity and for an ellipse e < 1

i can't find anything useful in my books and don't even know where to start.

any help would be awesome! thanks!

-skiz

 

[indr0008]

David Morin's book on mechanics explains very clearly on how to derive this equation

 

[skiz]

hmm i don't have david morin's book on mechanics..

any tips on how to go about deriving this? am i supposed to use the geometry of an ellipse?

bah

 

[vjraghavan]

I assume that you are doing a course in Introductory Mechanics. The book by Kleppner & Kolenkow is really good for such a course. However in that book, the authors have begun from Law of conservation of energy and angular momentum and have derived the polar form of the equation. I believe that this is a good way to do this as it begins from conservation principles.

 

[tiny-tim]

Welcome to PF!

Hi skiz! Welcome to PF!

Is this a mechanics question (find the orbit of a particle in an electric or gravitational field), or a geometry question (find the equation for an ellipse)?

Assuming it's mechanics, start with Newton's second law, and remember that the force perpendicular to the "radius" vector is zero.

 

[skiz]

hey tim, thanks for the welcome!

yeah its a mechanics course. Our first 6 months are split between "Classical Mechanics" and "Modern Physics/Relativity"

i find modern physics and relativity really interesting and easy to grasp but classical mechanics is kicking my ass...

 

[tiny-tim]

Hi skiz!

Just remember that nearly all classical mechanics boils down to good ol' Newton's second law …

force in a particular direction = (rate of) change of momentum in that direction ​

… and in each case you just have to work out which direction gives you the best information (in this case, it's the "transverse" direction).

 

[mutafa2008]

please anyone help me?

please anyone help me to find the equation of eccentricity of object moves in elliptical orbit